Repton model viscosity

Dependence of viscosity, reduced by the cube of molar mass, on the number of entanglements per chain. Filled circles are data from the Repton model of Section 9.6.2, courtesy of... 

Viscosity of linear polymer calculated from Monte Carlo simulations. Filled circles are repton model data from M. Rubinstein, Phys. Rev. Lett. 59,1946 (1987), with data range extended by D. Shirvanyants and open squares are Evans-Edwards model data from J. M. Deutsch and T. L. Madden,... 

A discretized version of the reptation model is proposed. The tube is modeled by a one-dimensional lattice, and the polymer is modeled by a cluster of walkers, called reptons, on this lattice. Each repton represents a part of the chain. Reptons are allowed to hop between neighboring sites in such a way that the cluster always remains connected. The fluctuations in tube length correspond to cluster length fluctuations in the repton model and are not pre-averaged. In the experimentally accessible range of molecular weights M, the repton model predicts the diffusion coefficient and viscosity 0.1 ... 

Fig. 4. Repton model predictions of the viscosity hq as a function of cluster size N. Straight lines are best fits of the higher JV parts of the plot. Their slopes are 3.22 for coordination number 2=2, 3.36 for 2=6 and 3.52 for 2= 12.

Fig. 4.5 Repton model prediction for the viscosity r] as function of the nmnber of reptons per chain N for different values of z, as indicated. The slope varies from 3.22 (z = 2) to 3.52 (z = 12), (from Ref 28).

---